make changes

Author: pathywang

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,4 +1,5 @@
 from typing import List
+cache = {}
 
 
 def ways_to_make_change(total: int) -> int:
@@ -14,6 +15,11 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
     """
+    key = (total, tuple(coins))
+
+    if key in cache:
+        return cache[key]
+    
     if total == 0 or len(coins) == 0:
         return 0
 
@@ -29,4 +35,7 @@ def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
                 intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
                 ways += intermediate
             count_of_coin += 1
+
+    cache[key] = ways
     return ways
+